Milan progressed the third qualifying round of this season's Europa League by beating Rovers 2-0 at Tallaght Stadium last Thursday.
Ibrahimovic opened the scoring on the night with a trademark finish 23 minutes into the contest, before Hakan Calhanoglu's stunning second half-strike wrapped up a comfortable victory for Stefano Pioli's men.
The ex-Sweden international, who signed a new one year contract at San Siro last month, also hit the crossbar and caused problems for the Rovers defence throughout the 90 minutes, defying his age once again as he approaches his 39th birthday on October 3.
Byrne has now admitted that Ibrahimovic was the main difference between the two sides, praising the veteran frontman for his movement and how he managed to make a huge contribution while still managing to conserve plenty of energy.
"For such a big man, he was like a ghost on the pitch, you couldn't pick him up. His movement for his goal was fantastic," the Rovers midfielder told OTB Sports.
"That is just what top players do, you can keep them quiet for the whole game and then they pop up in one moment. I thought throughout the game he was brilliant, just dictating the game without running around."
Asked what makes Ibrahimovic such a special player, Byrne responded: "From such a young age, he was good - it is a natural gift that he has that he can move so well for a big man.
"But going through top clubs, it is not enough - you have to add little parts to your game depending on what managers want you do.
"He has done that over the years and his record speaks for itself, but I think that he has got better with experience."
The Irishman added on the Milan frontman's aggressive approach the game and Roversgiving a good account of themselves on the European stage: "I think he was giving the lads a little bit! You don't mind that - it made it competitive.
"It made it that they weren't taking us lightly, they were right up for the game, they pressed us and played the game properly. We played the game properly too, because if you switch off then they can hit you for six or seven.
"Us being at our best and them being bang at it - they beat us 2-0. Obviously, we are disappointed with the result but it is not the worst in the world."
Ibrahimovic will be forced to sit out Milan's third round qualifying tie against Bodo/Glimt on Thursday night after testing positive for coronavirus, and will now observe a two-week period in quarantine before returning to action.